A selection of the results of a theoretical investigation of the properties of interfaces and surfaces of the wide-gap III-V nitride semiconductors is reviewed. The electronic properties of wurtzite heteroepitaxial interfaces of AlN and GaN, incorporating the effects of strain, are discussed. In particular, we find that this interface is of type I and have calculated the valence-band offset to be -0.57 eV. The surface energies and atomic geometries of the 2 X 2 reconstructions of the (0001) face of GaN are also presented. In conditions which are rich in a given species, an adatom reconstruction of that species is found to be the most energetically favorable : for gallium-rich conditions, the reconstruction with a gallium adatom on a T-3 Site is the most stable, while for nitrogen-rich conditions the reconstruction with a nitrogen adatom on the H-3 site is energetically the most favorable.